## Leonhard Euler

## Benoit Mandelbrot

Eda Paksoy

Benoit B. Mandelbrot (November 20, 1924 - October 14, 2010), was a Polish-born French-American mathematician. He was mainly interested in the practical sciences and is recognized for his contribution to fractal geometry. He was also the one who coined the word "fractal" and referred to himself as a “fractalist.” He showed how fractals can occur in many different places in both mathematics and in nature.

In 1936, while he was a child, Mandelbrot's family emigrated to France from Warsaw, Poland. There, his uncle Szolem Mandelbrojt, who was Professor of Mathematics at the Collège de France, took responsibility for his education. His uncle didn’t support pure or applied mathematics. Mandelbrot attributed much of his success to this unconventional education. He said that it allowed him to think in ways that might be hard for someone who, through a conventional education, is strongly encouraged to think in standard ways. It also allowed him to develop a highly geometrical approach to mathematics, which gave him unique perspectives into mathematical problems.

After World War II, Mandelbrot studied mathematics in Paris and the United States and received a master's degree in aeronautics from the California Institute of Technology. He spent most of his career in both the United States and France, having dual French and American citizenship. In 1958, he began a 35-year career at IBM (International Business Machines Corporation) and periodically took leaves of absence to teach at Harvard University.

At Harvard University, Mandelbrot began to study Julia sets that were unchanging under certain transformations of the complex plane. In 1975, Mandelbrot coined the term fractal to describe these structures in his book Fractals, Shape, Chance and Dimension. Mandelbrot used the term "fractal" as it derived from the Latin word "fractus," defined as broken or shattered glass.

Simply, fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop.

Because of his access to IBM's computers, Mandelbrot was one of the first to use computer graphics to display fractal geometric images. This led to his discovery of the Mandelbrot set in 1980. He showed how visual complexity can be created from simple rules. He said that things typically considered to be "rough," a "mess," or "chaotic," such as clouds or shorelines, actually had a "degree of order." In 1982, Mandelbrot expanded his ideas in The Fractal Geometry of Nature.

Mandelbrot explains fractals by saying “It's marvelous, a very simple formula explains all these very complicated things. So the goal of science is starting with a mess, and explaining it with a simple formula, a kind of dream of science.”

Mandelbrot created the first-ever "theory of roughness," and he saw "roughness" in the shapes of mountains, coastlines; the structures of plants, blood vessels, and lungs; the clustering of galaxies. His purpose was to create a mathematical formula to measure the overall "roughness" of such objects in nature. Mandelbrot emphasized the use of fractals as realistic and useful models for describing many "rough" phenomena in the real world. He concluded that real roughness is often fractal and can be measured.

Mandelbrot saw financial markets as an example of "wild randomness" and developed several approaches for modelling financial fluctuations. After his study of U.S. commodity markets in relation to cotton futures, he taught economics and applied sciences at Harvard.

Towards the end of his career, he was a Sterling Professor of Mathematical Sciences at Yale University, where he was the oldest professor in Yale's history to receive tenure. During his career, he received over 15 honorary doctorates and served on many science journals, along with winning numerous awards.

Mandelbrot died from pancreatic cancer at the age of 85 in Cambridge, Massachusetts on 14 October 2010. His autobiography, The Fractalist: Memoir of a Scientific Maverick, was published in 2012, soon after his death.

References:

“Benoit Mandelbrot - Biography.” Maths History, mathshistory.st-andrews.ac.uk/Biographies/Mandelbrot/.

“Benoit Mandelbrot.” Encyclopedia Britannica, Encyclopædia Britannica, Inc., www.britannica.com/biography/Benoit-Mandelbrot.

Figure References:

“'Fractal' Mathematician Benoit Mandelbrot Dies Aged 85.” BBC News, BBC, 17 Oct. 2010, www.bbc.com/news/world-europe-11560101.

McClure, Mark. “Chaos and Fractals: Computational Approach.” Geometric Iteration and Fractal Geometry, www.marksmath.org/classes/Fall2017ChaosAndFractals/chaos_and_fractals/subsection-geometric_iteration.html.

NSF 01-20 - Mandelbrot Set, www.nsf.gov/pubs/2002/nsf0120/nsf0120_man.html.